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MathNet 2016-part-05 — 184 problems (EN–VI) Question 143

Math Olympiad Vault · MathNet 2016-part-05 — 184 problems (EN–VI)

Question 143

Boris takes a taxi to his home but falls asleep when the taxi is halfway to his house. He wakes up when the remaining part of his journey is equal to half the distance covered by the taxi while he was asleep.
If the fraction of the journey for which he slept is $\frac{1}{n}$, what is the value of $n$?